Design of Single, Multiple, and Scaled Nonlinear Springs for Prescribed Nonlinear Responses

Nonlinear springs enhance the performance of many applications including prosthetics, microelectromechanical systems devices, and vibration absorption systems. This paper describes a comprehensive approach to developing compliant elements of prescribed nonlinear stiffness. It presents a generalized methodology for designing a single planar nonlinear spring for a prescribed load-displacement function. The spring’s load-range, displacement-range, and nonlinear behavior are matched using this methodology, while also addressing stress, material, stability, and space constraints. Scaling guidelines are included within the optimization to relax the constraints on the solution space. Given the nonlinear nature of the spring designs, this paper further investigates their function in new configurations. Compliant structures with customized elastic properties are constructed by exploiting symmetry and by arranging nonlinear springs in series and/or in parallel. Scaling guidelines are used to meet new design specifications. The guidelines allow adjustment of load-range, displacement-range, material, and the overall footprint while preserving the spring’s nonlinear behavior without violating stress constraints. Various examples are provided throughout the paper to demonstrate the implementation and merit of these design approaches.